Classification and refined singularity of positive solutions for nonlinear Maxwell equations arising in mesoscopic electromagnetism

This paper is a continuation of [13], where we studied the existence and other analytic properties of positive radial solutions for a system of nonlinear Maxwell equations in the plane R2, which arises in the modelling of mesoscopic scale electromagnetic phenomena. In this paper we derive local estimates of singular positive solutions, based on which a classification theorem of general positive solutions is established. The refined singularity of general positive solutions is also investigated by employing the theory of infinite dimensional dynamical systems.